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The Czochralski method is the primary technique for single-crystal silicon production. However, anomalous states such as crystal loss, twisting, swinging, and squareness frequently occur during crystal growth, adversely affecting product quality and production efficiency. To address this challenge, we propose an enhanced multimodal fusion classification model for detecting and categorizing these four anomalous states. Our model initially transforms one-dimensional signals (diameter, temperature, and pulling speed) into time–frequency domain images via continuous wavelet transform. These images are then processed using a Dense-ECA-SwinTransformer network for feature extraction. Concurrently, meniscus images and inter-frame difference images are obtained from the growth system's meniscus video feed. These visual inputs are fused at the channel level and subsequently processed through a ConvNeXt network for feature extraction. Finally, the time–frequency domain features are combined with the meniscus image features and fed into fully connected layers for multi-class classification. The experimental results show that the method can effectively detect various abnormal states, help the staff to make a more accurate judgment, and formulate a personalized treatment plan for the abnormal state, which can improve the production efficiency, save production resources, and protect the extraction equipment. [ABSTRACT FROM AUTHOR]

The thermal-fluid coupling phenomenon of silicon melt is significant in the growth process of silicon single crystals. Complex convection affects the temperature and concentration distribution of the silicon melt. Therefore, establishing and solving the thermal-fluid coupling model of silicon melts is crucial to optimizing the crystal growth process and improving crystal quality. Traditional numerical simulation methods have limitations in regard to optimization, control, and real-time monitoring. Physics-Informed Neural Network (PINN) does not require model discretization, after training, it can make predictions quickly, showing potential for industrial applications. However, when solving practical industrial coupling models, PINN often struggles to converge due to large parameter values and significant gaps between solution variables. Moreover, solving the thermal-fluid coupling model with PINN can be treated as a multitask problem, where the gradients of different equations interfere with each other, leading to gradient confusion, slow convergence, or even divergence. Therefore, this paper proposes a gradient normalized PINN (GNPINN) for solving the thermal-fluid coupling model of silicon melt. GNPINN balances the contribution of each task, ensuring a more equitable training speed between different tasks to stabilize the training process of the coupling model. This paper considers the thermal-fluid coupling model of silicon melt under different rotation conditions. GNPINN can accurately and comprehensively capture the complex temperature, velocity, and pressure distribution of silicon melt compared with other methods. Additionally, the experimental results uncover the flow and heat transfer properties of silicon melt, validating the effectiveness and industrial applicability of GNPINN. [ABSTRACT FROM AUTHOR]

In the process of silicon single-crystal preparation, the timely identification and adjustment of abnormal conditions are crucial. Failure to promptly detect and resolve issues may result in a substandard silicon crystal product quality or even crystal pulling failure. Therefore, the early identification of abnormal furnace conditions is essential for ensuring the preparation of perfect silicon single crystals. Additionally, since the thermal field is the fundamental driving force for stable crystal growth and the primary assurance of crystal quality, this paper proposes a silicon single-crystal growth temperature gradient trend classification algorithm based on multi-level feature fusion. The aim is to accurately identify temperature gradient changes during silicon crystal growth, in order to promptly react to early growth failures and ensure the stable growth of high-quality silicon single crystals to meet industrial production requirements. The algorithm first divides the temperature gradient trend into reasonable categories based on expert knowledge and qualitative analysis methods. Then, it fuses the original features of actual production data, shallow features extracted based on statistical information, and deep features extracted through deep learning. During the fusion process, the algorithm considers the impact of different features on the target variable and calculates mutual information based on the difference between information entropy and conditional entropy, ultimately using mutual information for feature weighting. Subsequently, the fused multi-level feature vectors and their corresponding trend labels are input into a Deep Belief Network (DBN) model to capture process dynamics and classify trend changes. Finally, the experimental results demonstrate that the proposed algorithm can effectively predict the changing trend of thermal field temperature gradients. The introduction of this algorithm will help improve the accuracy of fault trend prediction in silicon single-crystal preparation, thereby minimizing product quality issues and production interruptions caused by abnormal conditions. [ABSTRACT FROM AUTHOR]

Monocrystalline silicon is an important raw material in the semiconductor and photovoltaic industries. In the Czochralski (CZ) method of growing monocrystalline silicon, various factors may cause node loss and lead to the failure of crystal growth. Currently, there is no efficient method to detect the node loss of monocrystalline silicon at industrial sites. Therefore, this paper proposed a monocrystalline silicon node-loss detection method based on multimodal data fusion. The aim was to explore a new data-driven approach for the study of monocrystalline silicon growth. This article first collected the diameter, temperature, and pulling speed signals as well as two-dimensional images of the meniscus. Later, the continuous wavelet transform was used to preprocess the one-dimensional signals. Finally, convolutional neural networks and attention mechanisms were used to analyze and recognize the features of multimodal data. In the article, a convolutional neural network based on an improved channel attention mechanism (ICAM-CNN) for one-dimensional signal fusion as well as a multimodal fusion network (MMFN) for multimodal data fusion was proposed, which could automatically detect node loss in the CZ silicon single-crystal growth process. The experimental results showed that the proposed methods effectively detected node-loss defects in the growth process of monocrystalline silicon with high accuracy, robustness, and real-time performance. The methods could provide effective technical support to improve efficiency and quality control in the CZ silicon single-crystal growth process. [ABSTRACT FROM AUTHOR]

The growth process of silicon single crystal (SSC) is a typical batch production process, which has the characteristics of batch size, variety, complex process, and intensive technology. In order to accurately control the diameter and thermal field temperature of the Czochralski (Cz) SSC batch production process to ensure that the actual production requirements of electronic-grade SSC are met, this paper proposes an iterative learning-based batch process predictive control strategy Model Predictive Control - Iterative Learning Control - Extended State Observer (MPC-ILC-ESO). The control strategy consists of two parts. The time axis is a dual Model Predictive Control (MPC) controller, which is mainly used to deal with disturbance suppression and constraints in the production process of a single batch of SSC. The iterative axis is the Extended State Observer (ESO) based Iterative Learning Control (ILC) control algorithm to deal with uncertainty and disturbance estimation and compensation in the multi-batch production process. The control effects of the time axis and the batch axis are superimposed as the final controlled object input to ensure the crystal diameter and stable thermal field temperature. Finally, the effectiveness of the proposed control strategy is verified based on the data analysis of the semiconductor industry production process. [ABSTRACT FROM AUTHOR]

Silicon single crystal (SSC) quality monitoring and control has been a hot research topic in the field of the Czochralski crystal growth process. Considering that the traditional SSC control method ignores the crystal quality factor, this paper proposes a hierarchical predictive control strategy based on a soft sensor model for online control of SSC diameter and crystal quality. First, the proposed control strategy considers the V/G variable (V is the crystal pulling rate, and G is the axial temperature gradient at the solid–liquid interface), a factor related to crystal quality. Aiming at the problem that the V/G variable is difficult to measure directly, a soft sensor model based on SAE-RF is established to realize the online monitoring of the V/G variable and then complete hierarchical prediction control of SSC quality. Second, in the hierarchical control process, PID control of the inner layer is used to quickly stabilize the system. Model predictive control (MPC) of the outer layer is used to handle system constraints and enhance the control performance of the inner layer. In addition, the SAE-RF-based soft sensor model is used to monitor the crystal quality V/G variable online, thereby ensuring that the output of the controlled system meets the desired crystal diameter and V/G requirements. Finally, based on the industrial data of the actual Czochralski SSC growth process, the effectiveness of the proposed crystal quality hierarchical predictive control method is verified. [ABSTRACT FROM AUTHOR]

Multi-furnace scheduling simultaneously is an important part to increase productivity and reduce the production cost in single crystal silicon enterprises. In the restrained power consumption requirements environment, the optimal sequencing of process operation start-time for single crystal furnaces is a challenging problem. To solve this problem, the scheduling model of multi-furnace scheduling is established in this paper to minimize the maximum completion time. Then, an improved DE algorithm called the multi-strategy individual adaptive mutation differential evolution algorithm (MSIADE) is presented to address the scheduling model. In the improved DE algorithm, the different dimensional and multi-strategy mutation operations are adopted to refrain the algorithm from the local optimal, then the different mutation factors are assigned to each individual through the rank of fitness function value to strengthen the exploration ability of the MSIADE algorithm. Simulation experiments results based on the standard test functions and the established scheduling model show the feasibility in the established model and the effectiveness in the proposed algorithm. [ABSTRACT FROM AUTHOR]

Considering the widely existing processing time uncertainty in the real-world production process, this paper constructs a fuzzy mathematical model for the silicon single crystal production batch scheduling problem to minimize the maximum completion time. In this paper, a two-stage hybrid optimization algorithm (TSHOA) is proposed for solving the scheduling model. Firstly, the improved differential evolution algorithm (IDE) is used to solve the order quantity allocation problem of silicon single crystal with different sizes to obtain the quantity of silicon single crystal rods with different sizes produced by different types of single crystal furnaces. Secondly, the variable neighborhood search (VNS) algorithm is adopted to optimize the order quantity sequencingof batch production processes. Finally, simulations and comparisons demonstrate the feasibility of the model and the effectiveness of TSHOA. [ABSTRACT FROM AUTHOR]

Aiming at the online monitoring of key variables during the growth process of Czochralski (Cz) silicon single crystal (SSC), this paper is aimed to propose a performance-driven hierarchical control strategy based on soft-sensing model. To this end, corresponding sub-models based on the mechanism model and industrial data are first established. Then, the two linear forms of them are combined to arrive at the mechanism- and data-driven hybrid variable weighted stacked autoencoder random forest (M-HVW-SAE-RF) soft sensing model. Among them, the stacked autoencoder (SAE) network is utilized to extract the deep features of the data, and the random forest (RF) is employed to realize the regression prediction of the target variable. Secondly, for the problem of model uncertainty, based on the identification for control (I4C) theory, a performance-driven hierarchical control strategy is established on the basis of the model predictive control-adaptive disturbance rejection control (MPC-ADRC). The main goal is to achieve the best output performance of the actual control system and to implement online monitoring of crystal size and V/G. Finally, based on the analysis of the production process data of the semiconductor industry, the effectiveness of the proposed control strategy is verified. [ABSTRACT FROM AUTHOR]

The power consumption in the process of silicon single crystal growth is huge, so the power load must be limited to a specific range to ensure the safe and stable operation on the silicon single crystal furnace. This article establishes a two-objective mathematical model for the multi-furnace optimal scheduling problem in silicon single crystal production process. The first objective is to minimize the maximum completion time of silicon single crystal growth process on multi-furnaces, and the second objective is to minimize the maximum power consumption obtained by the multi-furnace operation together. A disturbed non-dominated sorting particle swarm optimization combined with genetic algorithm (DNSGPSO) is proposed to solve the multi-objective optimization problem. Through simulation analysis of actual growth data, the effectiveness of the proposed model and the superiority of the algorithm are verified. • This article expands the research fields of actual industrial production scheduling problems. • This article can provide theoretical reference for the planning and scheduling of production tasks. • This article establishes a multi-objective scheduling model for the silicon single crystal production process to increase production efficiency and decrease production cost. • This article proposed DNSGPSO algorithm to solve the multi-objective optimization problem. [ABSTRACT FROM AUTHOR]

In the process of growing 300 mm diameter silicon single crystal by Czochralski method, uniform diameter is the key to obtain high quality silicon single crystal. It is found in production practice that too high pulling speed causes the phenomenon of twisting crystal at uniform diameter growth stage, which leads to the crystal line fracture and then crystalloblast, and it is unfavorable to uniform diameter growth. In this paper, the origin of the twisting crystal in the growth of ø300 mm silicon single crystal was analyzed by the combination of numerical simulation and theory analysis. For varying pulling speed, the correlation between crystal diameter and melt temperature distribution was established, the affecting factors on twisting crystal were obtained. The results show that with the increase of pulling speed, the supercooling zone is generated on the free surface of the melt, and continue to expand. The generation of supercooling zone is the main reason leading to twisting crystal. A method for identifying the maximum stable pulling speed is presented based on the numerical simulation of the finite element thermal field, and the method of varying the rotation speed of the crystal is proposed to improve the free surface temperature distribution of the melt, so as to avoid the crystal twisting. The results provide a guidance to the thermal field design of large diameter silicon monocrystalline growth. [ABSTRACT FROM AUTHOR]

The optimal operation of the semiconductor silicon single crystal (SSC) growth in an industrial single crystal furnace is contingent upon the precise measurement of both the crystal diameter and melt temperature. The Czochralski (CZ) silicon single crystal growth process (CZ-SSCGP) is a phase transition process from solid to liquid that takes place in a high-temperature, enclosed furnace designed for single crystal growth. The direct measurement of crystal diameter and melt temperature using sensors can pose a challenge due to the physical limitations of the furnace. This study introduces a novel approach for modeling clustering based on data that integrate fuzzy C-means (FCM) and deep belief network (DBN) techniques. The proposed method aims to estimate the online crystal diameter and melt temperature. The objective of this approach is to efficiently and precisely derive the CZ-SSCGP model. In order to address the negative impact of nonequilibrium properties of data on the model, it is advisable to employ FCM to produce numerous subsets of data that exhibit comparable operating conditions. This is especially important because data change over time and are different in different working situations. In order to enhance the precision of the fitting process for crystal diameter and melt temperature, we amalgamate the output outcomes of DBN that have been constructed for each individual subset. It is imperative to address the nonlinear and time-varying features manifested by the engineering data. Industrial data are utilized for conducting diverse data experiments and comparative analyses. The process takes into account the data’s susceptibility to contamination by outliers. The findings suggest that the method put forth exhibits superior precision and enhanced resilience in predicting crystal diameter and melt temperature compared to alternative modeling approaches. [ABSTRACT FROM AUTHOR]

Czochralski (Cz) silicon single crystal growth process is a large delay, nonlinear dynamic time-varying system with complex physicochemical reactions, multi-field and multi-phase coupling, and its modeling and control has always been a problem in the automatic control field. In this paper, a hybrid modeling method based on the data-driven model and mechanism model is proposed, and applied to the Cz silicon crystal growth process modeling. Firstly, to simplify the model complexity and improve the model accuracy, the crystal growth process model is divided into the energy transfer model and a hydrodynamic and geometric model. Here, a Hammerstein–Wiener model based on a long short-term memory network (LSTM-Hammerstein–Wiener) is established for the energy transfer process with multiple heat transfer links and hysteresis effect. Further, a novel robust LSTM-Hammerstein–Wiener model is proposed by introducing the M-estimation method, which avoids the effect of the outliers on model robustness. Secondly, the proposed robust LSTM-Hammerstein–Wiener is combined with the hydrodynamic and geometric model to obtain the hybrid model between the heater power and the crystal diameter. Meanwhile, the crystal diameter error compensation model is established to reduce the unmodeled dynamics of the mechanism model, thereby improving the accuracy of the hybrid model. Besides, the proposed hybrid model is applied to the model-free adaptive control of silicon single crystal diameter. Finally, various data experiment results based on actual operating data verify the effectiveness of the proposed hybrid model. [ABSTRACT FROM AUTHOR]

The growth process of Czochralski (Cz) silicon single crystal is a dynamic time-varying system with nonlinearity, strong coupling, large hysteresis, and uncertain model. Traditional model-based control methods are difficult to achieve satisfactory crystal growth control effects, and it is difficult to ensure that the crystal quality meets the actual process requirements. Therefore, from the perspective of data-driven modeling and control, this paper proposes a model predictive control method for the crystal growth process with a V/G soft-sensing model for measuring crystal quality. First, because the V/G value to measure crystal quality is difficult to obtain directly, a hybrid variable weighted stacked autoencoder random forest (HVW-SAE-RF) soft-sensing model based on data-driven V/G value is established. Here, the HVW-SAE is used to extract the deep quality-related features of the measurable process data, and the RF is used for the regression prediction of the SAE output layer; Second, using the dual closed-loop control strategy, the inner loop is based on the HVW-SAE-RF soft-sensing model of the V/G value, and the predictive PI control method is used to control the V/G value closely related to the crystal quality within a reasonable range, and the outer loop based on real-time estimation of V/G values to achieve nonlinear model predictive control (NMPC) of crystal diameter; finally, the effectiveness of the proposed method is verified based on the industrial production process data of silicon single crystal. [ABSTRACT FROM AUTHOR]

A new control strategy combing the Finite Element Method (FEM) with the control method is proposed to study the control of crystal growth process in this article. In the proposed control strategy, the crystal diameter control loop and the crystal temperature control loop are designed respectively to meet the requirements on crystal diameter and crystal temperature distribution. In the crystal diameter control loop, a bio-heuristic model based PID controller is designed to control crystal diameter. In the crystal temperature control loop, considering the undetectable characteristic of temperature distribution inside crystal, the control of crystal temperature distribution is transformed into the control of a key monitoring point in crystal and the constraint of crystal temperature gradient, and a model reference adaptive temperature controller is designed to achieve the control of the monitoring point temperature. Simulation results show that the crystal diameter and the temperature of the monitoring point are controlled well. Furthermore, the internal temperature distribution inside crystal is constrained within a reasonable range, avoiding the excessive thermal stress and dislocation defects. The proposed control strategy solves the problem of the traditional crystal growth system which cannot control crystal temperature, providing a new way for growing high-quality single silicon crystal. [ABSTRACT FROM AUTHOR]

During the growth of silicon single crystals, it is critical to detect the liquid level of the silicon melt to ensure their high-quality production. Because noise statistics are difficult to determine in measured values of the liquid level, a particle filter (PF) with unknown statistics has been presented to estimate the liquid level. However, this approach leads to inaccurate results due to sample impoverishment. To alleviate this problem, we propose an intelligent PF method with an adaptive Metropolis–Hastings (M-H) resampling strategy. To accomplish this, we first design an M-H resampling strategy with two proposed distributions to resample low-weight particles. These distributions randomly select high-weight particles for the Gaussian mutations or high-weight and low-weight particles for crossover operations, so as to promote the movement of low-weight particles to high-probability regions. We also construct a self-adaptive function to further improve the overall particle quality, which is used to calculate the selection probability of these two proposed distributions according to the proportion of low-weight particles in all of the particles. Finally, the liquid level is estimated according to the particles after the modified resampling strategy is applied. A comparative evaluation of the proposed method with the adaptive genetic particle filter (AGPF) and the firefly algorithm intelligence optimized particle filter (FAIOPF) is conducted. Some results of the simulation and the practical experiment are presented; they indicate the proposed method offers accuracy improvements in the liquid-level estimation during the silicon crystal growth. More specifically, compared with the AGPF and the FAIOPF, the mean absolute error (MAE) of the proposed method has been reduced by approximately 53.3% and 99.5%, respectively. [ABSTRACT FROM AUTHOR]

In the process of silicon single-crystal growth, the detection of melt level is an important step to ensure that the grown silicon single crystal is of high quality. Since there exist many mechanical motions, chemical interactions, thermal convection, and so on, it is extremely difficult to obtain the noise statistics of the liquid-level data. To attain a high-accuracy detection of liquid level with unknown noise statistics, we present an extended set-membership-based particle filter (PF). The key points are as follows. We construct a nonlinear state-space model for liquid-level detection system based on the kinematic principle and laser triangulation measurement principle and cast the detection problem of the liquid level into a state estimation problem. Based on this model, we use the extended set-membership estimation theory to generate an ellipsoid set that contains the true value of the liquid-level state. To overcome the difficulty of drawing particles under the case of unknown statistics noise, we draw particles from a Gaussian distribution in the obtained ellipsoidal set. In order to resample particles when the measurement noise statistic is unknown, we introduce a cost function to obtain the weights of the particles, and the ultimate estimation of liquid level is calculated by the weighted particles after the resampling procedure. Comparing with the extended Kalman PF (EPF) and the cost-reference PF (CRPF), the proposed algorithm has higher estimation accuracy. Some simulation and experiment results are presented to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

A new control structure with constant pulling speed for growing high-quality crystal in the Czochralski (CZ) method is presented in this brief. In this control structure, the pulling speed is not involved in the controlling of crystal diameter and only the temperature is used as the control quantity. Due to the time delay and the nonlinearity relationship are commonly involved between the temperature and crystal diameter, which make the diameter control difficult and complicated, a generalized predictive controller (GPC) based on the stacked sparse autoencoder (SSAE) is proposed under the new control structure. The time delay is obtained by using the correlation identification algorithm, the input order and output order are determined by the Lipchitz quotients algorithm, and the prediction model is trained by SSAE. Combining the SSAE with the nonlinear GPC algorithm, the control law of the temperature is calculated for diameter control. The simulation result verifies the correctness of the proposed control algorithm. The experimental result indicates that the new control structure with constant pulling speed is more conducive to growing high-quality crystal, avoiding the fluctuation of pulling speed. The proposed SSAE-based GPC algorithm can accurately track the reference diameter. The studies in this brief provide a feasible strategy for growing large size and high-quality crystal in the CZ method. [ABSTRACT FROM AUTHOR]

This paper proposes a alternate physics-informed neural network (PINN) with a two-stage training strategy to solve the thermoelastic coupling in the growth of Czochralski silicon single crystal. Particularly, neural networks with a two-stage training strategy are established for solving partial differential equations in the thermoelastic coupling model. At present, PINN still faces challenges in solving coupling models. Especially for the imbalance between and within equations in the coupling model. To solve this problem, this paper splits the model into two independent systems with their coupling term exchanged in the alternating iteration. Then, the imbalance inside a single solution of the coupling model is solved by the proposed two-stage training strategy, and the imbalance between solutions is avoided by alternative iterations. Experimental results show that the proposed alternate two-stage PINN (ATPINN) can accurately simulate the temperature and displacement in the thermoelastic coupling model. Compared with the finite element results, the error of temperature prediction and displacement prediction is acceptable. The numerical results demonstrate the feasibility and performance of the ATPINN. Furthermore, ATPINN can be extended to any type of coupling model, especially for coupling models with large differences in the magnitudes of the loss functions. The codes developed in this manuscript are publicy available at https://github.com/callmedrcom/ATPINN. [ABSTRACT FROM AUTHOR]

The reliable assessment of the operational status during the silicon single crystal growth process is a prerequisite for ensuring system safety and improving crystal quality. However, in the actual silicon single crystal growth process, due to limitations in manpower, material resources, financial resources, and current technical methods, the establishment of monitoring models is still in its infancy. To address this issue, this paper proposes a hybrid deep belief network (HDBN) algorithm aided by the digital twin (DT) model to achieve real-time monitoring of equipment operational status. Firstly, this study constructs the DT model based on the basic principles of crystal growth, mainly to achieve high-precision simulation of the actual silicon single crystal growth process and generate abnormal data for the equipment. This operation can expand the sample set, enhance the diversity and coverage of data, and effectively solve the problem of insufficient sample size. Secondly, this study uses the variational mode decomposition (VMD) algorithm to decompose the dataset composed of obtained abnormal and normal data, and constructs sub-deep belief network (DBN) for the decomposed subsequences to capture deep feature information at different frequencies of the data. Subsequently, based on the concept of ensemble learning, the outputs of each sub-DBN network are used as inputs to construct the overall DBN network, achieving monitoring of the equipment operational status. Through the combination of VMD decomposition and DBN networks, this algorithm can better capture the frequency characteristics and time-domain features of the signal, enhancing monitoring accuracy. Experimental results show that this algorithm can accurately identify abnormal equipment states, effectively improve monitoring performance, and is of significant importance for the optimization and control of the semiconductor-grade silicon single crystal growth process, contributing to increased production efficiency and product quality. [ABSTRACT FROM AUTHOR]